Mathematics Commons^™

Enumeration Of Independent Sets In Graphs, James Alexander

Theses, Dissertations and Culminating Projects

An independent set is one of the most natural structures in a graph to focus on, from both a pure and applied perspective. In the realm of graph theory, and any concept it can represent, an independent set is the mathematical way of capturing a set of objects, none of which are related to each other. As graph theory grows, many questions about independent sets are being asked and answered, many of which are concerned with the enumeration of independent sets in graphs. We provide a detailed introduction to general graph theory for those who are not familiar with the …

Tower Families Of Ribbon Graphs, Jordan Keller

Honors Capstones

No abstract provided.

Construction And Analysis Of Magic Squares Of Squares Over Certain Finite Fields, Stewart Hengeveld

Theses, Dissertations and Culminating Projects

This thesis presents results of the research on the study of Magic Squares of Squares over certain finite fields. The research is motivated by an open question, which is still not answered: "Does there exist a 3 x 3 magic square with all nine entries being distinct perfect squares of integers?" Instead of directly trying to answer this challenging question, this research attempts to answer a parallel question: "Does there exist a 3 x 3 magic square with all nine entries being distinct perfect squares modulo a prime number p?" Equivalently, the question can be restated as, "Does there exist …

The Persistence Of Infectious Diseases In Metapopulations, Jonathan Calvin Hayes

Theses, Dissertations and Culminating Projects

Mathematical models provide a great deal of information about the dynamics of disease spread. In this paper, we use stochastic simulation to investigate spontaneous disease extinction and réintroduction in a SIR model. We begin by investigating path to extinction and time to extinction in single population models, and then expand to a multipopulation model linked with linear migration. We have found that in a single population model, it is more effective to use random pulse vaccinations less per year at a higher removal rate. We have expanded this result by developing a vaccination strategy giving one large, well timed pulse …

The Number Of Ways To Write N As A Sum Of ` Regular Figurate Numbers, Seth Jacob Rothschild

Renée Crown University Honors Thesis Projects - All

See Document for Abstract

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Department of Math & Statistics Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

Genomic Analysis Of Immune Response Against Vibrio Cholerae Hemolysin In Caenorhabditis Elegans, Surasri N. Sahu, Jada Lewis, Isha Patel, Serdar Bozdag, Jeong H. Lee, Joseph E. Leclerc, Hediye Nese Cinar

Mathematics, Statistics and Computer Science Faculty Research and Publications

Vibrio cholerae cytolysin (VCC) is among the accessory V. cholerae virulence factors that may contribute to disease pathogenesis in humans. VCC, encoded by hlyA gene, belongs to the most common class of bacterial toxins, known as poreforming toxins (PFTs). V. cholerae infects and kills Caenorhabditis elegans via cholerae toxin independent manner. VCC is required for the lethality, growth retardation and intestinal cell vacuolation during the infection. However, little is known about the host gene expression responses against VCC. To address this question we performed a microarray study in C. elegans exposed to V. cholerae strains with intact and deleted hlyA …

Human Gene Copy Number Spectra Analysis In Congenital Heart Malformations, Aoy Tomita-Mitchell, Donna K. Mahnke, Craig Struble, Maureen E. Tuffnell, Karl D. Stamm, Mats Hidestrand, Susan Harris, Mary A. Goetsch, Pippa Simpson, David P. Bick, Ulrich Broeckel, Andrew N. Pelech, James S. Tweddell, Michael Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

The clinical significance of copy number variants (CNVs) in congenital heart disease (CHD) continues to be a challenge. Although CNVs including genes can confer disease risk, relationships between gene dosage and phenotype are still being defined. Our goal was to perform a quantitative analysis of CNVs involving 100 well-defined CHD risk genes identified through previously published human association studies in subjects with anatomically defined cardiac malformations. A novel analytical approach permitting CNV gene frequency “spectra” to be computed over prespecified regions to determine phenotype-gene dosage relationships was employed. CNVs in subjects with CHD (n = 945), subphenotyped into 40 …

H-Colouring Bipartite Graphs, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-colouring of G (or homomorphism from G to H) is a function from the vertices of G to the vertices of H that preserves adjacency. H-colourings generalize such graph theory notions as proper colourings and independent sets. For a given H, k∈V(H) and G we consider the proportion of vertices of G that get mapped to k in a uniformly chosen H-colouring of G. Our main result concerns this quantity when G is regular and bipartite. We find numbers 0⩽a−(k)⩽a+(k)⩽1 with the property that for all such G, with high probability the proportion is …

Mathematics Classrooms At The Middle School Level: Does Grouping Make A Difference In Achievement, Adam Smieja

Mathematics Graduate Theses

This paper reviewed related research on student achievement based on how students were grouped, homogeneously or heterogeneously. Questions examined were whether students performed better in heterogeneous or homogenous groupings and to what extent did high-, average-, and low-ability students perform better in a particular group. Results showed that high-ability students in homogeneous groupings had higher gains in achievement when compared to their counterparts in heterogeneous groupings. However, gains for these high-ability students were not statistically significant. On the contrary, average-, and low-ability students did show statistically significant gains in achievement in the heterogeneous groupings. Yet, despite their effectiveness, implementation of …

The Zeta Function Of Generalized Markoff Equations Over Finite Fields, Juan Mariscal

UNLV Theses, Dissertations, Professional Papers, and Capstones

The purpose of this paper is to derive the Hasse-Weil zeta function of a special class of Algebraic varieties based on a generalization of the Markoff equation. We count the number of solutions to generalized Markoff equations over finite fields first by using the group structure of the set of automorphisms that generate solutions and in other cases by applying a slicing method from the two-dimensional cases. This enables us to derive a generating function for the number of solutions over the degree k extensions of a fixed finite field giving us the local zeta function. We then create an …

Approximation Of Elements Of Exponentials Of Differential Operators With Rational Quadrature, Daniel Elwood Lanterman

Master's Theses

We explore the possibility of improving the accuracy of approximations of elements of exponentials of differential operators, by using a rational function, instead of a polynomial function, as the interpolating function. Since a rational function behaves more like a decaying exponential function, it seems logical that the approximation should be more accurate. Through the use of high accuracy rational interpolants, we experiment with a numerical integration method to determine explicitly whether the error produced by a rational type approximation will indeed be less than that produced by a polynomial type approximation.

A Comparison Of Two Boundary Methods For Biharmonic Boundary Value Problems, Jaeyoun Oh

Master's Theses

The purpose of this thesis is to solve biharmonic boundary value problems using two different boundary methods and compare their performances. The two boundary methods used are the method of fundamental solutions (MFS) and the method of approximate fundamental solutions (MAFS). The Delta-shaped basis function with the Abel regularization technique is used in the construction of the approximate fundamental solutions in MAFS. The MFS produces more accurate results but needs known fundamental solutions for the differential operator. The MAFS can provide comparable results, and is applicable to more general differential operators. The numerical results using both methods are presented.

Rapid Approximation Of Bilinear Forms Involving Matrix Functions Through Asymptotic Analysis Of Gaussian Node Placement, Elisabeth Marie Palchak

Master's Theses

Technological advancements have allowed computing power to generate high resolution model s. As a result, greater stiffness has been introduced into systems of ordinary differential equations (ODEs) that arise from spatial discreti zation of partial differential equations (PDEs). The components of the solutions to these systems are coupled and changing at widely varying rates, which present problems for time-stepping methods. Krylov Subspace Spectral methods, developed by Dr. James Lambers, bridge the gap between explicit and implicit methods for stiff problems by computing each Fouier coefficient from an individualized approximation of the solution operator. KSS methods demonstrate a high order of …

Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu

Mathematics Faculty Publications

In this paper, we use Hermite cubic finite elements to approximate the solutions

of a nonlinear Euler-Bernoulli beam equation. The equation is derived

from Hollomon’s generalized Hooke’s law for work hardening materials with

the assumptions of the Euler-Bernoulli beam theory. The Ritz-Galerkin finite

element procedure is used to form a finite dimensional nonlinear program

problem, and a nonlinear conjugate gradient scheme is implemented to find

the minimizer of the Lagrangian. Convergence of the finite element approximations

is analyzed and some error estimates are presented. A Matlab finite

element code is developed to provide numerical solutions to the beam equation.

Some …

Computational Modeling And Numerical Methods For Spatiotemporal Calcium Cycling In Ventricular Myocytes, Michael Nivala, Enno De Lange, Robert J. Rovetti, Zhilin Qu

Mathematics, Statistics and Data Science Faculty Works

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain …

The Rook-Brauer Algebra, Elise G. Delmas

Mathematics, Statistics, and Computer Science Honors Projects

We introduce an associative algebra RB_k(x) that has a basis of rook-Brauer diagrams. These diagrams correspond to partial matchings on 2k vertices. The rook-Brauer algebra contains the group algebra of the symmetric group, the Brauer algebra, and the rook monoid algebra as subalgebras. We show that the basis of RB_k(x) is generated by special diagrams s_i, t_i (1 <= i < k) and p_j (1 <= j <= k), where the s_i are the simple transpositions that generated the symmetric group S_k, the t_i are the "contraction maps" which generate the …

Qualitative Analysis Of The Burgers-Huxley Equation, Jing Tian

Theses and Dissertations - UTB/UTPA

There are many well-known techniques for obtaining exact solutions of differential equations, but some of them only work for a very limited class of problems and are merely special cases of a few power symmetry methods. These approaches can be applied to nonlinear differential of unfamiliar type; they do not rely on special “tricks." Instead, a given differential equation can be made to reveal its symmetries, which are then used to construct exact solutions. In this thesis, we briefly present the theory of the Lie symmetry method for finding exact solutions of nonlinear differential equations, then apply it to the …

Assessing Changes In The Abundance Of The Continental Population Of Scaup Using A Hierarchical Spatio-Temporal Model, Beth E. Ross

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In ecological studies, the goal is often to describe and gain further insight into ecological processes underlying the data collected during observational studies. Because of the nature of observational data, it can often be difficult to separate the variation in the data from the underlying process or 'state dynamics.' In order to better address this issue, it is becoming increasingly common for researchers to use hierarchical models. Hierarchical spatial, temporal, and spatio-temporal models allow for the simultaneous modeling of both first and second order processes, thus accounting for underlying autocorrelation in the system while still providing insight into overall spatial …

On The Geometry Of Virtual Knots, Rachel Elizabeth Byrd

Boise State University Theses and Dissertations

The Dehn complex of prime, alternating virtual links has been shown to be non-positively curved in the paper "Generalized knot complements and some aspherical ribbon disc complements" by J. Harlander and S. Rosebrock (2003) [7]. This thesis investigates the geometry of an arbitrary alternating virtual link. A method is constructed for which the Dehn complex of any alternating virtual link may be decomposed into Dehn complexes with non-positive curvature. We further study the relationship between the Dehn space and Wirtinger space, and we relate their fundamental groups using generating curves on surfaces. We conclude with interesting examples of Dehn complexes …

Periodic Solutions And Positive Solutions Of First And Second Order Logistic Type Odes With Harvesting, Cody Alan Palmer

UNLV Theses, Dissertations, Professional Papers, and Capstones

It was recently shown that the nonlinear logistic type ODE with periodic harvesting has a bifurcation on the periodic solutions with respect to the parameter ε:

u' = f (u) - ε h (t).

Namely, there exists an ε0 such that for 0 < ε < ε0 there are two periodic solutions, for ε = ε0 there is one periodic solution, and for ε >ε0 there are no periodic solutions, provided that....

In this paper we look at some numerical evidence regarding the behavior of this threshold for various types of harvesting terms, in particular we find evidence in the negative or a conjecture regarding the behavior of this threshold value.

Additionally, we look at analagous steady states for the reaction-diusion …

Formulæ For The Number Of Partitions Of N Into At Most M Parts (Using The Quazi-Polynomial Ansatz), Andrew Sills, Doron Zeilberger

Mathematical Sciences: Faculty Publications

The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for p_m(n) for any desired m. We do this to demonstrate the power of “rigorous guessing” as facilitated by the quasi-polynomial ansatz.

Valuation Of Financial Derivatives Subject To Liquidity Risk, Yanan Jiang

UNLV Theses, Dissertations, Professional Papers, and Capstones

Valuation of financial derivatives subject to liquidity risk remains an open problem in finance. This dissertation focuses on the valuation of European-style call option under limited market liquidity through the dynamic management of a portfolio of assets. We investigate liquidity from three perspectives: market breadth, depth, and immediacy. We present a general framework of valuation based on the optimal realization of a performance index relative to the set of all feasible portfolio trajectories. Numerical examples are then presented and analyzed that show option price increases as the market transitions from liquid to less liquid state. Furthermore, buying and selling activities, …

Ignoring The Spatial Context In Intro Statistics Classes - And Some Simple Graphical Remedies, Nathan Voge

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Statistical data often have a spatial (geographic) context, be it countries of the world, states in the US, counties within a state, cities across the globe, or locations where measurements have been taken. However, most introductory statistics books do not even suggest that such data often are not independent from location, but rather are eected by some spatial association. Remedies are simple: Display data via various map views and brie y discuss which additional information can be extracted from such a graphical representation. In this report, we will visit a variety of popular introductory statistics textbooks and show how some …

Validation Study: A Case Study Of Calculus 1 (Math 1210), Abibat Adebisi Lasisi

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This report discusses the process of assessing the validity of a test. We provide an analysis of the validation study of a test administered to the first semester calculus students at Utah State University in the Fall 2011 semester. The results of our analysis suggest that the test has some measurement relevance. This implies that the subject contents of the test correlate with the syllabus of the course. Thus, the measurement has some learning level relevance. Our analysis also revealed that the measurement has a high reliability coefficient which signifies some internal consistency of the mea- surement. The relevancy and …

A Collection And Analysis Of Local Middle Grade Math Projects For The Common Core, Lynnette Checketts

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The State of Utah has changed the mathematics core curriculum several times over the past decade. The latest change was the adoption of the Common Core State Standards introducing both grade level content standards and standards of mathematical practice that emphasize how students are to study and reason with mathematics at all grade levels. According to state officials, these standards require more mathematical reasoning, problem solving, and deeper understanding than previous core curriculum documents. One way to address this change is for teachers to educate using projects during their instruction as unit starters, daily lessons, and for evaluation purposes. Yet …

American Mathematical Association Of Two Year Colleges Reform Policies In Practice : Implementing Standards In Classroom Instruction For Basic Skills Mathematics At One Four-Year College In New Jersey, Patricia J. Garruto

Theses, Dissertations and Culminating Projects

High school graduates continue to enter post-secondary education lacking in basic mathematical skills and thus not academically prepared to enroll in college-level mathematics courses (ACT, 2010). Although it can be argued that those mathematical concepts should have been mastered in grades K-12, educating those students in basic skills mathematics has become the responsibility of universities and colleges. Two publications of the American Mathematical Association of Two Year Colleges (AMATYC), Crossroads (1995) and Beyond Crossroads (2006) set forth standards for mathematics programs and courses offered to students during their first two years of postsecondary education, which includes basic skills programs. Those …

Serving Two Masters : A Study Of Quantitative Literacy At Small Colleges And Universities, Jodie Ann Miller

Theses, Dissertations and Culminating Projects

The past twenty years have seen a growing interest in promoting quantitative literacy (QL) courses at the college level. At small institutions, financial realities impose limitations on faculty size and therefore the variety of courses that may be offered. This study examined course offerings below calculus at four hundred twenty-eight small colleges to gain a thorough understanding of the approaches to developing QL among the general population of undergraduate students. Using a three-phase model of examining progressively narrower subsets of QL programs at small institutions, document-based data from college catalogs and communication with mathematics program chairs were studied to summarize …

Elliptic Curves Of High Rank, Cecylia Bocovich

Mathematics, Statistics, and Computer Science Honors Projects

The study of elliptic curves grows out of the study of elliptic functions which dates back to work done by mathematicians such as Weierstrass, Abel, and Jacobi. Elliptic curves continue to play a prominent role in mathematics today. An elliptic curve E is defined by the equation, y^₂ = x³ + ax + b, where a and b are coefficients that satisfy the property 4a³ + 27b² = 0. The rational solutions of this curve form a group. This group, denoted E(Q), is known as the Mordell-Weil group and was proved by Mordell to be isomorphic …

Spectrum Estimation With Uniformly And Stochastically Sampled Data: Some Challenges And Strategies., Radhendushka Srivastava Dr.

Doctoral Theses

No abstract provided.